Methods and systems for capturing coordinates of points—or locations—of real-world surfaces for input into computer-aided design (CAD) software are in widespread use. The points may be on a two-dimensional (2D) surface or on the exterior of a three-dimensional (3D) object. The process of inputting coordinates of points of a 2D medium or a 3D object into a computer memory is commonly called digitizing. For example, a digitizing tablet may be used to input XY coordinates of sampled points on a 2D image—such as a photograph, blueprint, or pencil-sketched drawing—in order to build a CAD or other computer graphics representation of the salient geometric features of the image.
Similarly, a “cloud of points” may be sampled from the 3D surface of a physical object to build a data representation (or model) of the geometry of the physical object in a computer memory. Each sampled point may be represented by an XYZ coordinate triple. In a more sophisticated representation, the cloud of points may be converted into vertices of abutting planar polygonal patches which approximate the surface of the object. In a more sophisticated representation, the cloud of points may be converted into abutting curved polygonal patches. Each patch, whether planar or curved, may be defined by a mathematical bivariate polynomial or rational function—such as in the NURBS surfaces commonly used in computer graphics. In special cases, 3D data entry may rely on real-world measurements where the generic geometric shape (e.g., circle, sphere, cube, cylinder, etc.) of a real-world object is known, but the dimensions of the shape must be determined by physically measuring the coordinates of one or more points to quantify the shape.
Numerous approaches exist for measuring real-world surface points. For planar media, various 2D digitizing tablets are commercially available which are commonly used in computer-aided drafting and design. The two most common input devices are a hand-held pen-like stylus with a pointing tip, and a manually moveable cursor—also called a puck. The movable cursor may have a reticle scribed into a transparent plate which can be moved over the surface of the tablet or a planar medium on the tablet. A common form of a reticle is pair of crosshairs. The reticle may include an indicator, such as an arrow tip or the intersection of the crosshairs, which indicates the particular surface point to be measured by the moveable cursor.
A probe may be used to input of points on the surface of a 3D object. Such a probe may have a pointer, tip, or other indicator for indicating an individual location on the object. The indicator may be a sharp conical pointer, a spherical tip of known radius, a grooved tip for tracing edges, or a roller of known radius.
Generally, the location of the indicator on the probe, cursor, or puck is measured in two or three dimensions by a coordinate measuring system, referred to herein as a tracker. The tracker may not track the indicator directly, but instead track sensible markers spaced apart from the indicator. In many cases, placing a sensible marker exactly at the location of the indicator would be problematic, because the size or the opacity of the marker may obscure the indicator from view. This problem may be avoided by tracking two or more markers positioned with a known geometrical relationship with respect to the indicator, so the location of the indicator may be computed from the locations of the markers.